Skewness in portfolio allocation: a comparison between different mean-variance and mean-variance-skewness investors

Abstract: We investigate the problem of portfolio allocation using an expected utility framework where investors' preference for positive skewness of returns is introduced. We develop a three-parameter generalized utility function that can be used to capture the full spectrum of absolute and relative risk aversions from CARA to DRRA in comparable settings. We approximate the utility function with the use of a Taylor series expansion truncated at different points to include or exclude the preference for skewness. We then find different optimal mean-variance and mean-variance-skewness portfolios and compare them with each other by looking at their absolute distances in space and differences in certainty equivalent, across investors with different levels of risk aversion and different kinds of risk aversions. We find that the mean-variance and mean-variance-skewness solutions to the portfolio choice problem diverges more as the overall level of risk aversion increases, as well as when investors exhibits utility functions with decreasing relative risk aversion (DRRA) and decreasing absolute risk aversion (DARA). Differences in certainty equivalent between the mean-variance optimization and mean-variance-skewness optimizations can be economically significant for highly risk averse investors and DARA/DRRA investors.